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SEMANTIC SIMILARITY EVALUATION MODEL IN CATEGORICAL DATABASE
GENERALIZATION
1
2
Liu Yaolin ,
Martin Molenaar ,
Menno-Jan Kraak
2
1
School of Resource and Environmental Science
Wuhan University, Wuhan, 430070, P.R. China
2
Department of Geo-Informatics
International Institute for Aerospace Survey and Earth Science
7500 AA, Enschede,The Netherlands
Email {yaolin, Molenaar, Kraak}@itc.nl}
Commission IV, WG IV/3
KEY WORDS: Hierarchical structure, Similarity Model, Categorical Database, Classification System,
ABSTRACT
Database generalization process will be used to derive a new database with less detail for some application purposes from a single
detailed database. In a database generalization process, semantic similarity measures among objects and among object types play a
key role in object aggregation process. In this paper a generalization procedure will be developed based on object aggregation. The
decision to aggregation objects will be based on the geometric properties of the objects, on their spatial relationships and on their
thematic similarity. Normally, this similarity among objects acts as decisive rule that controls the generalization operations. This
paper focuses on semantic similarity evaluation model for categorical database generalization. It presents a semantic evaluation
model after reviewing current similarity models. The models are based on classification hierarchies, set theory, and attribute structure
of classes. It is a computation model and can not only be used to compute the similarity between objects at same level, or at different
levels, but also the similarity between object types at the same level and at different level.
1. INTRODUCTION
set theory, hierarchy structure and attribute structure of class.
The similarity measures among objects and among object types
play a key role in object aggregation in database generalization.
The
aggregating two objects not only depends on the
geometric properties of the two objects, but also the thematic
The paper is organized as following. First, the brief review is
given; secondly, the basic concepts for similarity measure are
given and followed by the computing similarity model is
proposed; finally an example is used to test the model.
properties of the two objects. Using Set theory, Tversky (1977)
defines a similarity measure in terms of matching process. This
measure produces a similarity value that is not only the result
2.
BASIC CONCEPTS
of the common, but also the result of the different
Some basic concepts must be clear before discussing similarity
computing model.
characteristics between objects, which is in agreement to an
2.1 Class, Object Type and Object
information theory definition of similarity (Lin,D 1998,
Rodriquez and Egenhofer 1999, Bishr, 1997, Chakroun et
In this paper, the class and object type have the same meaning.
A class or object type determines a set of attributes to form its
al,2000, Rodríguez and M. Egenhofer, 1999, Rodríguez, M.
attribute structure. Each class c j or object type c
Egenhofer and Rugg, 1999). Although many models of
own attribute structure List (c j ) as following:
similarity are defined in the literature, the similarity measure
method based on set theory, hierarchy structure and attribute
structure of class is still lack. This paper mainly discusses the
similarity measure method in the database generalization used
j
has its
List(c j )={A 1 ,…A i ,…A n }
A i denotes one of the attributes of class c j .
Each attribute
will have a name, a domain that will be specified by defining
Symposium on Geospatial Theory, Processing and Applications,
Symposium sur la théorie, les traitements et les applications des données Géospatiales, Ottawa 2002
the range of the attribute values and scale type of the domain
which indicates whether these values are from a nominal, an
ordinal, an interval or ratio scale. An attribute A i can be
specified by a three tuple (Molenaar 1998):
However there are still lack of formalization of classification
hierarchy and aggregation hierarchy based on Set theory and
properties of class. In the following part, the formalizations of
classification
A i ={NAME(A i ), SCALETYPE(A i ), DOMAIN(A i )}
For each object which belong to class c
j
, the attribute
hierarchy
and
aggregation
hierarchy
are
discussed.
The object types in a geo-spatial model are normally
determined by classification hierarchy and aggregation
structure defined by a class specifies the description structure
hierarchy. Changing classification hierarchy and aggregation
of the object. A value is assigned to every attribute in the
hierarchy will results in changing geo-spatial model associated
attribute structure of object. For any object, its direct class is
with database, and in turn changing the contents of the database.
unique and lowest in a classification hierarchy since different
Changing the attribute structure and extension of classes at
classes have different attribute structures. These values must
different level in classification hierarchy and aggregation
fall within the range of the attribute domain, which must be
hierarchy associated with a database will induce a new
defined prior to the actual assignment of attribute values.
classification hierarchy and aggregation hierarchy and define a
new data model of database and rebuild the corresponding
Class
A1
A2
…
An
contents of database.
Let S be the set of objects {o 1 ,o 2 , o 3 ,…,o i }in space, U be
Object i
Figure 1
a1
a2
…
an
the set of classes {c 1 ,c 2 ,c 3 ,…,c j } for the database space.
Before formalizing classification and aggregation hierarchy, the
relations between classes must be identified.
Diagram representing the relations
between objects, classes and attributes ( after Molenaar 1998 )
Let c i , c
j
∈ U be two arbitrary spatial classes, there should be
no objects that belong to the extensions of the two different
Each object has an attribute structure list containing one value
classes of U. Based on the definition of classification hierarchy
a j for every attribute of its class. The thematic description of
last chapter and relations among classes, we can formalize
an object can now be specified by its class (which specifies the
attributes of the object) together with the list of attribute values.
classification hierarchy with intension and extension of the
2.2
classes.
Intension and Extension of A Class
•
c
ψ
i
c
Ext(c i ) ∩ Ext(c
the value of a combination of attributes. The condition specifies
a subset of the set containing all the possible combinations of
among classes symbolized by
the values of the attributes, denoted as Int(c j ), while the set of
with c j );
all the objects that belong to c
j
with the same attribute
structure is commonly identified as the extension of the class
•
≡
ci
Ext(c j ) of c
Hierarchy
•
⊆
ci
≤c
j
), (c i is consistent
abstraction and generalization (Smith and Smith 1977,
symbolized by
j
) of c
is equal to
i
and c i is identical to c
j
);
c j ;( Relations of inclusion among classes
ci
of c
≡ ),(Ext(c i
c j , only if Ext(c i ) ⊆ Ext(c j ), denoted as
databases and knowledge bases, especially in relation to data
Yee,Leung, Kwong,S.L. nad He J.Z 1999, Molenaar 1996).
ψ
c j , only if Ext(c i )=Ext(c j ), denoted as
symbolized by
Formalizing Classification Hierarchy and Aggregation
The class hierarchy has been studied for many years in
if
c i = c j ; (Relations of equivalence among classes
c j , denoted as Ext(c j ).
2.3
only
) ≠ φ ;( Relations of consistent
The intension of a class c j can be expressed as a condition for
j
,
j
⊆ ), (Ext(c i ) of c i
and c i belongs to c j )
include Ext(c j )
or
•
⊂
ci
c j , if Ext(c i ) ⊂ Ext(c j ), denoted as c i <c
c j . We also call c i a sub-class of c
and c
j
a
j
super-class of c i . (Relations of complete inclusion
among classes symbolized by
⊂
c i completely include Ext(c
) of c
j
the properties of the hierarchical structure. A, B and C in Figure
2 represent the different branches in the hierarchical structure.
For later use, they are called sub tree. T in the same Figure is
called the top of the structure and c i are object or object type.
), (Ext(c i ) of
j
and c
T
i
completely belongs to c j ).
•
c
φ
≠
i
c
j
T
, only if Ext(c
i
)
∩
Ext(c
j
)=
g
.( Relations of disjunction among classes
symbolized by
≠ ),
between c i and
c j , and c i is different from c j ).
j
if and only if the
extension of c i is subsumed by the extension of
c9
c6
c5
c10
c8
c17
Example of a hierarchical structure
Figure 2
is a partial binary relation on U, called the
`Belong to’ relation, and (U,
c7
c15
c j . We call
c i ‘IS-A’ c j .
≤c
C
c14
(there is no common object
A class c i is included by a class c
Obviously,
B
A
≤ c) is a partially ordered set that
The semantic similarity matrix represents the similarity
between object types.
we call a classification hierarchy. The process of formalization
of classification hierarchy depicts how the object types (classes)
Table 1
Example of semantic similarity matrix
and super object types can be formed into a hierarchical
structure. For creation of a new super object type in the
classification hierarchy there will be:
SIMILARIT
Y
Sub-type1
Sub-type1
If any A, B ∈ H and no D ∈ H satisfying Ext(D)
=Ext(A)
∪ Ext(B),
∪
…
type2
11
s
14
s
15
s
24
s
25
Sup-type1
s
17
s
27
…
…
…
…
…
…
…
…
s
s
44
45
s
47
s
57
…
type2
Ext(B), LIST(D) =LIST(A)
∩ LIST(B) and D ∈ H,
…
…
type1
then generate such a class D, and let
Ext(D) =Ext(A)
Sub-type2
type1
…
s
•
…
s
55
…
…
…
Sup-type1
noted as IS-A links;
s
77
…
…
…
…
…
…
…
…
…
…
The upward connections from objects to classes and classes to
super classes are is-a links, which express that an object is an
instantiation of a class and that a class is a special case of more
Where:
sub-type1 etc denote different elementary object types;
general super-class. At each level, the classes inherit the
type1,type2 denote different object types;
attribute structure of their super-classes at the next higher level
sup-type1etc denote (super) composite object type;
and propagate it normally with an extension to the next lower
level. At lowest level in the hierarchy are elementary objects
(Molenaar 1998).
2.4
Hierarchic Semantic Similarity Matrix
For a hierarchical structure as shown in Figure 2. a semantic
similarity matrix as shown in Table 1 can be defined based on
s ij denotes similarity value among object types.
The larger the value of an element in the matrix is, the more the
similarity between two object types that the element links is.
The matrix is symmetric and reflexive one, and has the
property that s ij is equal to s
ji
(s ij = s
ji
) and s ii is equal to
s
jj
(s ii = s
jj
=1) in the matrix. s
ji
is a value between o and
1.
This matrix shows the similarity among different levels of
object types. It will provide potential possibility to chose
objects of different types to be merged or aggregated. The
similarity matrix will be used as a look-up table for guiding or
governing the aggregation process of spatial objects in
and immediate super object types that subsumes them which
reflects difference properties between two given object types
and the other is the distance between immediate super object
types that subsumes two given object types and the top of
hierarchical structure which reflects the common properties of
two given object types.
For the second case, the distance
between immediate super object types that subsumes two given
object types and the top of hierarchical structure will be zero
semantics to a certain application.
The value of element s ij in the matrix can be given by expert
knowledge or by calculation (to be discussed in Section 6.3.2)
based on aggregation hierarchy and classification hierarchy.
since the two given object types belong to different sub tree
such as c 1 and c 15 in Figure 2. So this distance will be
replaced by the correlation value between two sub trees in the
3. COMPUTING MODEL OF SIMILARITY
Equation 2.
A computational model that assesses similarity among objects
and object types based on set theory, classification hierarchy
and attribute structure of class is proposed. There are three
distances. One is the distance (number of the link edges) from
immediate super object type that subsumes c i and c
j
s ij (c i
to the
top of a hierarchy such as object type g to top of the tree T in
l

 l + α (c , c ) * d + (1 − α (c , c )) * d
i
j
ci
i
j
cj

,c j )= 


β

(
,
)
*
(1 − α (ci , c j )) * d cj
+
+
β
α
c
c
d

i
j
ci
(1)
Figure 2 which represents common part of attribute structure
between two object types c
i
and c
j
. Another distance
(number of the link edges) from immediate super object type
that subsumes c i and c
j
to c i such as object type g to c 1 in
j
(c i and c
j
∈ same sub-tree)
∉ different sub-tree) (b)
immediate super object type that subsumes c i and c
d ci :
the shortest distance (number of the link edges) from
immediate super object type
super object type that subsumes c i and c
c
to c j such as
d cj :
object type g to c 5 in Figure 2 which represents the different
part of attribute structures between object type c i and c j (|
c
j
belonging to the same sub tree such as sub tree A in Figure 2
and the other is for two given object types belonging to two
different sub tree such as A and B as shown in Figure 2. For the
j
that subsumes c i and
to c i ;
the shortest distance (number of the link edges) from
immediate super object type that subsumes c i and
c
α:
j
to c j ;
a function of the distance (number of the link edge )
between immediate super object type that subsumes
c i and c j to the class c i and c j .
- c i |), The proposed model is shown in Equation 2. It
suits for two cases. One is for two given objects or object types
j
to the top of a hierarchy;
third is the distance (number of the link edges) from immediate
j
(a)
Where:
l:
the shortest distance (number of the link edge ) from
Figure 2 which represents the different part of attribute
structure between object type c i and c j (| c i - c j |). And the
(c i and c
β
:
correlation degree among different sub-trees, such as
similarity among agriculture land use, forest land use
and building up land use, and its value can be given
by experts based on application requirement.
first case, the model uses two types of distances to define the
A natural approach to comparing the degree of generalization
common and difference properties between the given object
between object types is to determine the distances from these
types. One is the distance between given objects or object types
object types to the immediate super object types that subsumes
them in a classification hierarchy as shown in Figure 1, that is,
extreme value 1 represents the case that the two entity classes
their least upper bound in a partially ordered set. In a sense, the
are completely the same, whereas the value 0 occurs when the
difference in the distances from these object types to the
two entity classes are completely different.
immediate super object types that subsumes them in a
classification hierarchy reflects the difference in attribute
structure between two object types. The
α (c i ,
c j ) can be
4.
EXAMPLE
An example for computing element of similarity matrix from
classification hierarchy is as following: Taking Figure 3 as
expressed as a function of the distance d ci and d cj . In order to
example to calculate the similarity among object types. The
α , the function (Equation (2)) is defined as
class code can be seen in appendix. The correlation value
get final values of
following:
among construction land, agriculture land and unused land that
is given by the experts is 0.5.
α
d ci

d + d
c j
(c i , c j )=  c i



d ci
1 −
d ci + d

(d ci
≤ d cj )
Land u se
(2)
C o n s t r u c tio n
(d c i >d cj )
c
j
R e s id e n T r a n s f o r …C u lt iv a t e F o r
ti l t
ti
d dl l d d
t
where:
d ci :
P ast … W a
t
san …
d
the shortest distance (number of the link edges) from
immediate super object type
c
d cj :
U n u sed
A g r ic u lt u r e
j
that subsumes c i and
t o w … R a il
r o a …I r .
d
il
D ry
l d
…W o o …N a t .
dl d
…
to c i ;
the shortest distance (number of the link edges) from
immediate super object type that subsumes c i and c
j
to c j .
Figure 3
Land use classification hierarchy before generalization
The computing result of similarity among object types based on
the model (see in Table 2.)
This similarity function yields values between 0and 1. The
5.
CONCLUSIONS
The computing model that has been proposed has taken set
theory, classification hierarchy and attribute structure into
account. It can be used to measure the semantic similarity
among object types in classification hierarchy. The example
shows that the computing result of the model are reasonable
and efficient. How to decide the correlation parameter
β
will
still need to research in the future work.
The authors would thanks the financial support from ITC,
Ministry of Education,P.R. China and State Bureau of
Surveying and Mapping.
6.
REFERENCES
Bishr, Y., 1997, Semantic aspects of interoperable GIS. ITC,
Publication No. 56, Enschede: International Institute for
Areospace Survey and Earth Sciences (ITC).
Chakroun,H., Benie,G.B., Oneill,N.T., and Desilets,J. 2000,
Spatial analysis weighting algorithm using Voronoi diagrams.
International Journal of Information Science, Vol.14,No.4
pp.319-336.
Lin, D. 1998,An Information theoretic definition of similarity
(eds.) International conference on amchine learning, ICML’98.
Molenaar, M., 1998,An Introduction to the Theory of Spatial
Object Modelling for GIS, Taylor & Francis Ltd. London.
Molenaar, M.,1996, The Role of Topologic and Hierarchical
Spatial Object Models in Database Generalization, In
Molenaar,M.(Eds.) Methods for the Generalization of
Geo-databases, Delft: Netherlands Geodetic Commission, New
Series, Nr 43,pp.13-36.
Rodríguez and M. Egenhofer, 1999, Putting similarity
assessment into context: matching functions with the user’s
intended operations. Modeling and Using Context,
CONTEXT'99, Trento, Italy. In: P. Bouquet, L. Serafini, Patrick
Brézillon, Massimo Benerecetti, and Francesca Castellani
(eds.), Lecture Notes in Computer Science, Vol. 1688,
Spiringer-Verlag, pp. 310-323,.
Rodríguez, M. Egenhofer, and R. Rugg , 1999, Assessing
semantic similarity among geospatial feature class definition
Interoperating Geographic Information Systems, Second
International Conference, INTEROP'99, Zurich, Zwitzerland.
In: . Vckovski, K. Brassel, and H.-J. Schek (eds.), Lecture
Notes in Computer Science, Vol. 1580, Springer-Verlag, pp.
189-202,.
124
125
13
Smith, J.M. and Smith, D.C.P, 1977, Database abstractions:
aggregation and generalization, ACM Transactions on Database
System, 2, pp.105-133
15
Tversky,A. 1977, Features of similarity. Psychological review,
84(40:PP.327-352).
Appendix
Land use classification (code)
1.
Agriculture Land
11
12
(100)
2.
Cultivated land
Rubber plantation
Other
Forest
131
Wood land
132
Shrubbery land
134
Young forestation land
135
Slashes
Water area
151
Rivers
153
Reservoir
154
Pond
156
Beaches and flats
158
Hydraulic building
Construction Land (200)
21 Residential quarters and industrial and mining land
111
Irrigated paddy fields
112
Rain fed paddy fields
211
113
Irrigated land
212
Residential quarters in rural areas
114
Dry land
213
Isolated industrial and mining
115
Vegetable plots
121
land
3.
Garden Land
Orchards
122
Mulberry fields
123
Tea fields
Area of cities and towns
Unused lands (300)
310
Waste lands
380
Others
Similarity Table
Table 2
S
111 112 113 114 115 121 122 123 124 125 131 132 134 135 151 153 154 156 158 211 212 213 110 120 130 150 210 310 380 100 200 300
111 1
0.7 0.7 0.7 0.7 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 1
112 0.7 1
0.7 0.7 0.7 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 1
113 0.7 0.7 1
0.7 0.7 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 1
114 0.7 0.7 0.7 1
0.7 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 1
115 0.7 0.7 0.7 0.7 1
0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 1
121 0.3 0.3 0.3 0.3 0.3 1
0.4 0.4 0.4 0.2 0.1 0.1 1
0.2 0.1
0.4 0.4 0.4 0.2 0.1 0.1 1
0.2 0.1
0.2 0.1
0.4 0.4 0.2 0.1 0.1 1
0.2 0.1
0.4 0.4 0.2 0.1 0.1 1
0.2 0.1
0.4 0.2 0.1 0.1 1
0.2 0.1
0.4 0.2 0.1 0.1 1
0.2 0.1
0.2 0.1
0.2 0.1 0.1 1
0.2 0.1
0.2 0.1 0.1 1
0.2 0.1
1
1
0.1 0.1 0.3 1
0.2
0.1 0.1 0.3 1
0.2
0.1 0.1 0.3 1
0.2
0.5 0.2 0.2 0.2 1
0.2 0.2 0.2 0.5 0.5 0.5 1
210 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 1
0.2 0.1 0.1 1
0.5 0.5 0.2 0.2 0.2 1
0.4 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.5 0.5 1
1
0.2 0.1
0.5 0.5 0.5 0.2 0.2 0.2 1
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.5 1
1
0.2 0.1 0.1 1
0.2 0.2 0.2 0.2 1
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.2 0.2 0.2 1
1
0.2 0.1
0.7 0.2 0.2 0.2 0.2 1
213 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.7 0.7 1
1
0.2 0.1 0.1 1
0.7 0.7 0.2 0.2 0.2 0.2 1
212 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.7 1
150 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 1
0.2 0.1
0.2 0.2 0.2 0.4 0.4 0.4 1
211 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 1
1
0.4 0.2 0.1 0.1 1
0.7 0.2 0.2 0.2 0.4 0.4 0.4 1
158 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.7 0.7 0.7 0.7 1
1
0.2 0.1
0.7 0.7 0.2 0.2 0.2 0.4 0.4 0.4 1
156 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.7 0.7 0.7 1
1
0.4 0.2 0.1 0.1 1
0.7 0.7 0.7 0.2 0.2 0.2 0.4 0.4 0.4 1
154 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.7 0.7 1
130 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 1
0.4 0.4 0.2 0.1 0.1 1
0.7 0.7 0.7 0.7 0.2 0.2 0.2 0.4 0.4 0.4 1
153 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.7 1
1
0.2 0.1
0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.4 0.4 1
151 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1
1
0.4 0.4 0.2 0.1 0.1 1
0.7 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.4 0.4 1
135 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.7 0.7 0.7 1
1
0.2 0.1
0.7 0.7 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.4 0.4 1
134 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.7 0.7 1
1
0.4 0.4 0.2 0.1 0.1 1
0.7 0.7 0.7 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.4 0.4 1
132 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.7 1
120 0.4 0.4 0.4 0.4 0.4 1
0.2 0.1
0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.4 1
131 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 1
1
0.4 0.4 0.4 0.2 0.1 0.1 1
0.7 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.4 1
125 0.3 0.3 0.3 0.3 0.3 0.7 0.7 0.7 0.7 1
1
0.2 0.1
0.7 0.7 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.4 1
124 0.3 0.3 0.3 0.3 0.3 0.7 0.7 0.7 1
1
0.4 0.4 0.4 0.2 0.1 0.1 1
0.7 0.7 0.7 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.4 1
123 0.3 0.3 0.3 0.3 0.3 0.7 0.7 1
1
0.2 0.1
0.7 0.7 0.7 0.7 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.4 1
122 0.3 0.3 0.3 0.3 0.3 0.7 1
110 1
0.4 0.4 0.4 0.2 0.1 0.1 1
0.2 0.2 0.2 1
0.2 0.2 0.2 0.2 1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.3 0.3 0.3 1
200 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 1
1
1
1
1
1
0.4 0.1
0.4 0.3
0.2 0.2 0.4 1
300 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.2 1
0.2
0.2 0.2 1
0.3 0.2 0.2 1
0.4 0.4 0.4 0.4 1
0.4 0.1
0.5 0.2 0.2 1
380 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.5 1
1
0.4 0.1
0.2 0.2 0.3 1
310 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 1
100 1
0.4 0.1
1
0.3
0.3 0.3 1